text:
\section{Introduction}\label{sec:intro}

Effective low-energy supersymmetry (SUSY) has many attractive features
and is widely expected to provide a more complete description of
phenomena at and above the electroweak scale than the Standard Model
(SM) of electroweak and strong interactions. In many SUSY models,
gauge coupling unification can easily be achieved, unlike in the SM or
non-SUSY versions of those models. Moreover, SUSY, when supplemented
by R-parity (or matter parity), offers an attractive candidate for
resolving the dark matter (DM) problem in the Universe.

On the other hand, SUSY, being a global symmetry, allows for
a whole multitude of possible effective models which otherwise would
suffer from the well-known hierarchy and fine-tuning problems. In the past,
most phenomenological studies focused on the Minimal Supersymmetric Standard Model
(MSSM) -- a supersymmetrized version of the
SM~\cite{susy-reviews}. More recently, a constrained version of the
MSSM (CMSSM)~\cite{kkrw94},
which includes a minimal supergravity (mSUGRA) model, has become more
popular by virtue of its relative simplicity and a small number of
free parameters. This is achieved by relating at the unification scale
the soft masses of the MSSM gauginos to a common value $\mhalf$, those
of the scalar partners of SM fermions to $\mzero$, the tri-linear
terms to $\azero$, in addition to $\tanb$ - the ratio of v.e.v.'s of
the neutral components of the two Higgs doublets.

One puzzling and unsatisfactory feature of the MSSM is the so-called
$\mu$-problem~\cite{mupb}: the Higgs/higgsino mass parameter is SUSY-preserving
but, on phenomenological grounds, it is expected to be of the same
order as soft SUSY breaking masses, $\mu\sim\msusy\simeq 1\mbox{ TeV}$. Various solutions
have been suggested, for example~\cite{gm88}.

A model that solves the $\mu$-problem of the MSSM in a simple way is
the Next-to-Minimal Supersymmetric Standard Model (NMSSM)~\cite{NMSSM1}. In the
NMSSM one adds a singlet chiral superfield S. The
explicit $\mu$ term is absent and the superpotential has only
dimensionless parameters and therefore the only new effective scale is the
one of the soft breaking terms $\msusy$. The $\mu$ parameter is
generated dynamically through the v.e.v. of the spin-0 component of
the singlet superfield.

At the phenomenological level, the presence of additional fields,
namely an extra CP-even and CP-odd neutral Higgs bosons, as well as a
singlino component of a neutralino, leads in general to a richer and more complex
phenomenology~\cite{NMSSM2,NLEP,NLHC,NHIGGS,NMHDECAY}, as well as cosmology,
in particular with respect to the domain wall problem~\cite{Abel1, Abel2, tadp}.

In analogy with the CMSSM, successful gauge coupling unification in
SUSY has provided motivation for considering a constrained version of
the NMSSM (CNMSSM)~\cite{CNMSSM1, NMSPEC}, which we will define below. Extensive
phenomenological investigations of the CNMSSM have been carried out
in~\cite{NMSSM2}.

On the other hand, the enlarged set of parameters makes a full exploration of the CNMSSM
even more challenging than in the case of the CMSSM. Traditional techniques of
sampling slices of the parameter space provide limited information and
are inadequate in a number of other aspects, for example in fixing
relevant SM parameters which may have much impact on the outcome, as
shown in~\cite{rtr1,rrt2,rrt3}.

More recently, it has been demonstrated that a Markov Chain Monte
Carlo (MCMC), or some other, scanning technique, coupled with Bayesian
statistics, can very efficiently
probe the whole parameter space and thus allow one to derive global
properties of the model under
investigation~\cite{al05,rtr1,rrt2,rrt3}.

Over the last few years, several studies using the Bayesian approach
have been performed of the CMSSM~\cite{al05,rtr1,rrt2,rrt3}, the
Non-Universal Higgs Mass Model (NUHM)~\cite{nuhm1}, the
MSSM~\cite{allanach+quevedo,hewett+rizzo} and large volume string
\cite{lvstring}.

One advantage of the Bayesian approach is that it allows quantitative
model comparison, using so called Bayes factors to see which model
best fits the data, be it selecting the sign of $\mu$ in the CMSSM to
picking a class of SUSY breaking.

In this paper we perform a Bayesian analysis of the CNMSSM. We explore
very broad ranges of the CNMSSM parameter and apply all most important
experimental and cosmological constraints, including all collider
limits, the branching ratio of $\bsgamma$, the difference
$\deltagmtwo$ between the experimental and SM values of the magnetic
moment of the muon, the LEP limits on sparticle and Higgs masses and
the 5 year WMAP limit on the relic abundance $\abundchi$ of the
lightest neutralino assumed to be the dark matter.
A full list
of constraints used and the exact numbers used in the analysis will be
given below.

Our main finding is that, somewhat contrary to initial expectations,
from the statistical point of view, most phenomenological and dark
matter features of the CNMSSM of crucial importance for experimental
tests closely resemble those of the CMSSM. In particular,
singlino-dominated LSP only appears in a very limited number of cases
that are not yet excluded by experimental bounds on the parameter
space.  Clearly, this will make it very challenging, although not
impossible, to distinguish the models at the LHC and in DM searches,
as we discuss below.

The paper is organized as follows: in Sec.~\ref{sec:overNMSSM} we
define and overview the NMSSM and the CNMSSM. In Sec.~\ref{sec:Bayes}
we describe our the statistical approach.  The results are presented in
Sec.~\ref{sec:CNMSSMpars} and we finish with our conclusions in
Sec.~\ref{sec:summary}.

\section{The NMSSM and the CNMSSM}\label{sec:overNMSSM}

The NMSSM superpotential contains a new superfield $S$ which is a singlet under the
SM gauge group $SU(3)_c \times SU(2)_L \times U(1)_Y$. (We use the
same notation for superfields and their respective spin-0 component fields for simplicity.)
\begin{equation}\label{2:Wnmssm}
W=
\epsilon_{ij} \left(
Y_u \, H_u^j\, Q^i \, u +
Y_d \, H_d^i\, Q^j \, d +
Y_e \, H_d^i\, L^j \, e \right)
- \epsilon_{ij} \lambda \,S \,H_d^i H_u^j +\frac{1}{3} \kappa S^3\,,
\end{equation}
where $H_d^T=(H_d^0, H_d^-)$, $H_u^T=(H_u^+, H_u^0)$, $i,j$ are
$SU(2)$ indices with $\epsilon_{12}=1$, while $\lambda$ and $\kappa$
are dimensionless couplings in the enlarged Higgs sector.

The superpotential in Eq.~(\ref{2:Wnmssm})
is scale invariant, and the EW scale will only appear through the soft SUSY
breaking terms in $\mathcal{L}_{\text{soft}}$, which in our conventions is
given by
\begin{align}\label{2:Vsoft}
-\mathcal{L}_{\text{soft}}=&\,
 {m^2_{\tilde{Q}}} \, \tilde{Q}^* \, \tilde{Q}
+{m^2_{\tilde{U}}} \, \tilde{u}^* \, \tilde{u}
+{m^2_{\tilde{D}}} \, \tilde{d}^* \, \tilde{d}
+{m^2_{\tilde{L}}} \, \tilde{L}^* \, \tilde{L}
+{m^2_{\tilde{E}}} \, \tilde{e}^* \, \tilde{e}
 \nonumber \\
&
+m_{H_d}^2 \,H_d^*\,H_d + m_{H_u}^2 \,H_u^* H_u +
m_{S}^2 \,S^* S \nonumber \\
&
+\epsilon_{ij}\, \left(
A_u \, Y_u \, H_u^j \, \tilde{Q}^i \, \tilde{u} +
A_d \, Y_d \, H_d^i \, \tilde{Q}^j \, \tilde{d} +
A_e \, Y_e \, H_d^i \, \tilde{L}^j \, \tilde{e} + \text{H.c.}
\right) \nonumber \\
&
+ \left( -\epsilon_{ij} \lambda\, A_\lambda S H_d^i H_u^j +
\frac{1}{3} \kappa \,A_\kappa\,S^3 + \text{H.c.} \right)\nonumber \\
&
- \frac{1}{2}\, \left(M_3\, \lambda_3\, \lambda_3+M_2\, \lambda_2\, \lambda_2
+M_1\, \lambda_1 \, \lambda_1 + \text{H.c.} \right) \,.
\end{align}
When the scalar component of $S$ acquires a VEV, $s=\langle S
\rangle$, an effective interaction $\mu H_d H_u$ is generated, with
$\mu \equiv \lambda s$.

In addition to terms from $\mathcal{L}_{\text{soft}}$, the
tree-level scalar Higgs potential receives the usual $D$ and $F$ term
contributions:
\begin{align}\label{2:Vfd}
V_D = & \, \,\frac{g_1^2+g_2^2}{8} \left( |H_d|^2 - |H_u|^2 \right)^2 +
\frac{g_2^2}{2} |H_d^\dagger H_u|^2 \, , \nonumber \\
V_F = & \, \,|\lambda|^2
\left( |H_d|^2 |S|^2 + |H_u|^2 |S|^2 + |\epsilon_{ij} H_d^i H_u^j|^2 \right)
+ |\kappa|^2 |S|^4
\nonumber \\
&
-\left( \epsilon_{ij} \lambda \kappa^* H_d^{i} H_u^{j}S^{*2} + \mathrm{H.c.}
\right) \,.
\end{align}

Using the minimization equations we can re-express the soft breaking
Higgs masses in terms of $\lambda$, $\kappa$, $A_\lambda$, $A_\kappa$,
$v_d=\langle H_d^0 \rangle$, $v_u=\langle H_u^0 \rangle$ (with
$\tanb=v_u/v_d$), and $s$:
 \begin{align}
m_{H_d}^2 = & -\lambda^2 \left( s^2 + v^2\sin^2\beta \right)
- \frac{1}{2} M_Z^2 \cos 2\beta
+\lambda s \tan \beta \left(\kappa s +A_\lambda \right) \,,
\label{2:minima:mh1}
\\
m_{H_u}^2 = & -\lambda^2 \left( s^2 + v^2\cos^2\beta \right)
+\frac{1}{2} M_Z^2 \cos 2\beta
+\lambda s \cot \beta \left(\kappa s +A_\lambda \right) \,,
\label{2:minima:mh2}
\\
\label{2:minima:ms}
m_{S}^2 = & -\lambda^2 v^2 - 2\kappa^2 s^2 + \lambda \kappa v^2
\sin 2\beta + \frac{\lambda A_\lambda v^2}{2s} \sin 2\beta -
\kappa A_\kappa s\,,
\end{align}

The boundary conditions at the grand unification scale $\mgut\simeq
2\times 10^{16}\mbox{ GeV}$ are analogous to those of the CMSSM, with the exception of $m_S$.
$\kappa$, $M_s$ and $s$ are fixed
by the minimization
equations~(\ref{2:minima:mh1})-(\ref{2:minima:ms}) which leads to five
continuous free parameters of the CNMSSM: $\mhalf$, $\mzero$,
$\azero$, $\tanb$ and $\lambda$, in addition to $\sgn(\mu)$.

The feature of not unifying $m_s$ with all the other soft scalar
masses at $\mzero$ gives one the necessary freedom to obtain, in the
limit $\lambda \to 0$, with $\lambda s$ fixed, the CMSSM plus a
singlet and a singlino field that both decouple from the spectrum, as
discussed in~\cite{NMSPEC}. For cosmological analyzes those extra
particles can still play an important role but from the particle
phenomenology point of view the model becomes indistinguishable from the
CMSSM. Also in this limit a singlino LSP is excluded since, being
completed decoupled, it can not annihilate into SM particles.

We also present the neutralino sector since the lightest neutralino
will, by assumption, play the r\^{o}le of dark matter. The mass term in
the Lagrangian is given by
\begin{equation}
\mathcal{L}_{\mathrm{mass}}^{\chi^0} =
-\frac{1}{2} (\Psi^0)^T \mathcal{M}_{\tilde \chi^0} \Psi^0 + \mathrm{H.c.}\,,
\end{equation}
with $\mathcal{M}_{\tilde \chi^0}$ given by a $5 \times 5$ matrix,
{\footnotesize \begin{equation}
  \mathcal{M}_{\chi^0} = \left(
    \begin{array}{ccccc}
      M_1 & 0 & -M_Z \sin \theta_W \cos \beta &
      M_Z \sin \theta_W \sin \beta & 0 \\
      0 & M_2 & M_Z \cos \theta_W \cos \beta &
      -M_Z \cos \theta_W \sin \beta & 0 \\
      -M_Z \sin \theta_W \cos \beta &
      M_Z \cos \theta_W \cos \beta &
      0 & -\lambda s & -\lambda v_u \\
      M_Z \sin \theta_W \sin \beta &
      -M_Z \cos \theta_W \sin \beta &
      -\lambda s &0 & -\lambda v_d \\
      0 & 0 & -\lambda v_u & -\lambda v_d & 2 \kappa s
    \end{array} \right),
  \label{neumatrix}
\end{equation}}
where $\mone$ ($\mtwo$) denotes soft the mass of the bino (wino) and
$\theta_W$ denotes the weak mixing angle.

\section{Outline of the method}\label{sec:Bayes}

Following the discussion of the previous Section, in the CNMSSM the
free parameters are given by
\beq
\theta = (\mhalf, \mzero,\azero, \tanb,\lambda),
\label{eq:cmssm}
\eeq
while we fix $\sgn(\mu)$= +1, which implies $s>0$. Furthermore,
without loss of generality we choose
$\lambda>0$~\cite{Cerdeno:2004xw}.

As the values of relevant SM
parameters, when varied over their experimental constraints, have an
impact on the observable quantities, fixing them would lead to
inaccurate results. Instead, here we incorporate them explicitly as
free parameters (which are then constrained using their measured
values), which we call {\em nuisance parameters} $\psi$, where
\beq
\psi = (\mtpole,m_b(m_b)^{\msbar}, \alpha_{s}(\mz)^{\msbar}).
\label{eq:nuis}
\eeq
In \eq{eq:nuis} $\mtpole$ denotes the pole top quark mass, while the
other two parameters: $\mbmbmsbar$ -- the bottom quark mass evaluated
at $m_b$ and $\alpha_s(M_Z)^{\overline{MS}}$ -- the strong coupling constant evaluated at
the $Z$ pole mass $\mZ$ - are all computed in the $\msbar$
scheme. Note that, in contrast to recent analyzes of the
CMSSM~\cite{al05,rtr1,rrt2}, we do not include among the nuisance
parameters the fine structure constant. This is because here we use
the Fermi constant, $\mZ$ and $\mW$ as input parameters, yielding
$\alpha_{\text{em}}$ as output.

Using notation consistent with previous analyzes we define our  eight dimensional
{\em basis  parameter} set as
\beq
m=(\theta,\psi)
\label{eq:basis}
\eeq
which we will be scanning simultaneously over. For
each choice of $m$ a number of colliders or cosmological observables
are calculated. These derived variables are denoted by
$\xi=(\xi_1,\xi_2,\ldots)$, which are then compared with the
relevant measured data $d$.

The quantity we are interested in is
the {\em posterior probability density function}, (or simply
posterior) $p(m|d)$ which gives the probability of the
parameters after the constraints coming from the data have been
applied. The posterior follows from Bayes' theorem,
\beq
p(m|d)=\frac{p(d|\xi) \pi(m)}{p(d)}
\eeq
where $p(d|\xi)$, taken as a function of $\xi$ for {\em
fixed data} $d$, is called the {\em likelihood} (where the
dependence of $\xi(m)$ is understood).  The likelihood is
the quantity that compares the data with the derived
observables. $\pi(m)$ is the {\em prior} which encodes our state of
knowledge of the parameters before comparison with the data. This
state of knowledge is then updated by the likelihood to give us the
posterior. $p(d)$ is called the {\em evidence} or {\em model
likelihood}, and in our analysis can be treated as a normalization
factor and hence is ignored subsequently for an example of how the
evidence can be used for model comparison purposes.

\begin{table}
\centering
\begin{tabular}{|c |}
 \hline
{CNMSSM parameters $\theta$}       \\ \hline
 $50 < \mhalf < 4 \mbox{ TeV}$ \\
 $50 < \mzero < 4 \mbox{ TeV}$ \\
 $|\azero| <  7\mbox{ TeV}$    \\
$2 < \tanb < 65$       \\
 $10^{-3}< \lambda <0.7$  \\ \hline\hline
{SM (nuisance) parameters $\psi$}       \\
\hline
{$160 < \mtpole < 190 \mbox{ GeV}$}\\
{$4 < m_b(m_b)^{\overline{MS}} < 5 \mbox{ GeV}$} \\
{$0.10 < \alpha_s(M_Z)^{\overline{MS}}  < 0.13$} \\ \hline
\end{tabular}
\caption{Initial ranges for our basis parameters
  $m=(\theta,\psi)$. }
\label{table:prior}
\end{table}

As our main prior we take very wide ranges of the CNMSSM parameters as
 given in Table~\ref{table:prior}, although we have performed a number
 of additional scans which will be discussed below. We adopt a flat
 prior in $\log \mhalf$, $\log \mzero$, $\azero$, $\tanb$ and
 $\lambda$.  Following Ref.~\cite{nuhm1}, we call this choice a {\em
 log prior}, as opposed to a completely {\em flat prior} used in some
 of our earlier analyzes where all the basis parameters are scanned
 with a flat measure.

As before~\cite{tfhrr1,nuhm1}, our rationale for this choice of priors
is that they are distinctively different. One reason why we apply
different priors to soft mass parameters only is that they play a
dominant r\^{o}le in the determination of the masses of the
superpartners and Higgs bosons. Another important reason is that flat
priors suffer from the ``volume effect'' by putting effectively too
much emphasis on larger values of scanned parameters, while the log
prior is more suitable for exploring smaller values of both $\mhalf$
and $\mzero$ which are anyway more natural in effective low-energy
SUSY models.  Therefore the choice of log priors appears to be
actually more suitable for revealing the structure of the model's
parameter space, similarly as in the CMSSM~\cite{tfhrr1} and the
NUHM~\cite{nuhm1}.

For the nuisance parameters we use flat priors (although this is not
important as they are directly constrained by measurements) and
apply Gaussian likelihoods representing the experimental observations
(see table~\ref{tab:meas}), as before~\cite{rtr1,rrt2,rrt3,nuhm1}.

We compute our mass spectra and observable quantities using the
publicly available NMSSMTools (version 2.1.1) that includes NMSPEC
with a link to Micromegas; for details see Ref.~\cite{NMSSMTools}. We
list the observables that the current version of NMSPEC, as linked
with statistical subroutines available in SuperBayeS allows us to
include in the likelihood function in Table~\ref{tab:measderived}. The
relic density $\abundchi$ of the lightest neutralino is computed with
the help of Micromegas, which is also linked to NMSPEC. We further use
the same code to compute the cross section for direct detection of
dark matter via its elastic scatterings with targets in underground
detectors but do not include it in the likelihood due to large
astrophysical uncertainties.

The likelihoods for the measured observables are taken as Gaussian
with mean $\mu$, experimental and theoretical errors (see the detailed
explanation in Refs.~\cite{rtr1,rrt2}). In the case where there only an
experimental limit is available, this is given, along with the
theoretical error.  The smearing out of bounds and combination of
experimental and theoretical errors is handled in an identical manner
to Refs.~\cite{rtr1,rrt2}, with the notable exception of the Higgs
mass and LEP limits on sparticle masses, which are calculated as a
step function with values of the cross section times branching ratio
(in the case of the Higgs) or mass that are within two standard
deviations of the experimental limit being accepted. Finally, any
points that fail to provide radiative EWSB, give us tachyons or the
LSP other than the neutralino are rejected.

As our scanning technique we adopt a ``nested sampling''
method~\cite{skilling-nsconv} as implemented in the
MultiNest~\cite{Feroz:2007kg} algorithm, which computes the Bayesian
evidence primarily but produces posterior pdfs in the process.
MultiNest provides an extremely efficient sampler even for likelihood
functions defined over a parameter space of large dimensionality with
a very complex structure. (See, {\it e.g.}, Refs.~\cite{tfhrr1,nuhm1}.)  This
aspect is very important for the model analyzed here since the
8-dimensional likelihood hyperspace is fragmented and features many
finely tuned regions that are difficult to explore with conventional
fixed grid, random scan or even MCMC methods. For a comparison of
CMSSM posterior maps obtained with a Metropolis-Hastings MCMC
algorithm~\cite{rtr1, rrt2, rrt3} and the MultiNest algorithm see
Ref.~\cite{tfhrr1}.

As we are using nested sampling in this study, the issue of stopping
criteria is handled differently from the MCMC case used in some
earlier paper~\cite{rtr1, rrt2, rrt3}. Our treatments follows
closely that presented in Appendix~A of Ref.~\cite{tfhrr1}. In
nested sampling one is calculating the Bayesian
evidence, defined by,
 \begin{equation}
 \mathcal{Z} \equiv  p(d) = \int_{0}^{1}\mathcal{L}(X)dX,
 \end{equation}
where $\mathcal{L}$ is the likelihood and $X$ the prior volume. One
can get the posterior in a nested sampling scan, but the principle
value calculated is the evidence. The stopping criteria takes into
account that in general one is proceeding through shells of increasing
iso-likelihood contours, with the set of ``live points" drawn from
within these contours. One can then define the stopping criterion as
taking the maximum likelihood point in the set of live points, see
Ref.~\cite{skilling-nsconv} ($\mathcal{L}_{\rm max}$) and calculating
the maximum change to the evidence it could make,
$\delta\mathcal{Z}_{i}=\mathcal{L}_{max}X_{i}$. Once this value goes
below a specified value (we take $\delta\mathcal{Z}<0.5$) the run is
terminated.

\begin{table}
 \centering
\begin{tabular}{|l | l l | l|}
\hline
SM (nuisance) parameter  &   Mean value  & \multicolumn{1}{c|}{Uncertainty} & Ref. \\
 &   $\mu$      & ${\sigma}$ (exper.)  &  \\ \hline
$\mtpole$           &  172.6 GeV    & 1.4 GeV&  \cite{cite:topmass} \\
$m_b (m_b)^{\overline{MS}}$ &4.20 GeV  & 0.07 GeV &  \cite{cite:mb} \\
$\alpha_{\text{s}}(M_Z)^{\overline{MS}}$       &   0.1176   & 0.002 &  \cite{cite:mb}\\
\hline
\end{tabular}
\caption{Experimental mean $\mu$ and standard deviation $\sigma$
 adopted for the likelihood function for SM (nuisance) parameters,
 assumed to be described by a Gaussian distribution.
\label{tab:meas}}
\end{table}

\begin{table}
\centering
\begin{tabular}{|l | l l l | l|}
\hline
Observable &   Mean value & \multicolumn{2}{c|}{Uncertainties} & Ref. \\
 &   $\mu$      & ${\sigma}$ (exper.)  & $\tau$ (theor.) & \\\hline
$\deltagmtwo \times 10^{10}$       &  29.5 & 8.8 &  1 & \cite{cite:g-2}\\
 $\brbsgamma \times 10^{4}$ &
 3.55 & 0.26 & 0.21 & \cite{cite:g-2} \\
$\brbtaunu \times 10^{4}$ &  $1.32$  & $0.49$  & $0.38$
& \cite{cite:CDF} \\
$\abundchi$ &  0.1099 & 0.0062 & $0.1\,\abundchi$& \cite{cite:WMAP} \\\hline
   &  Limit (95\%~\text{CL})  & \multicolumn{2}{r|}{$\tau$ (theor.)} & Ref. \\ \hline
$\brbsmumu$ &  $ <5.8\times 10^{-8}$ & \multicolumn{2}{r|}{14\%}  & \cite{cite:CDF2}\\
$\mhl$  & As implemented in NMSSMTool. & & & \cite{NMSSMTools} \\
sparticle masses  & As implemented in NMSSMTool. & & & \cite{NMSSMTools} \\ \hline
\end{tabular}
\caption{Summary of the observables used in the analysis. Upper part:
Observables for which a positive measurement has been
made. $\deltagmtwo$ denotes the discrepancy between
the experimental value and the SM prediction of the anomalous magnetic
moment of the muon $\gmtwo$. For central values of the SM input
parameters used here, the SM value of $\brbsgamma$ is
$3.11\times10^{-4}$, while the theoretical error of
$0.21\times10^{-4}$ includes uncertainties other than the parametric
dependence on the SM nuisance parameters, especially on $\mtpole$ and
$\alpha_s(M_Z)^{\overline{MS}}$.  For each quantity we use a
likelihood function with mean $\mu$ and standard deviation $s =
\sqrt{\sigma^2+ \tau^2}$, where $\sigma$ is the experimental
uncertainty and $\tau$ represents our estimate of the theoretical
uncertainty (see Ref.~\cite{rtr1} for details). Lower part: Observables for
which only limits currently
exist.  The likelihood function is given in
Ref.~\cite{rtr1}, including in particular a smearing out of
experimental errors and limits to include an appropriate theoretical
uncertainty in the observables in $\brbsmumu$. The limit on the light
Higgs mass $\mhl$ is applied in a simplified way, see text for details.
\label{tab:measderived}}
\end{table}

\section{Probability maps of CNMSSM parameters and observables}\label{sec:CNMSSMpars}

In this section we present our numerical results from global scans of
the CNMSSM parameter space.  We begin with the CNMSSM parameters and
next show probability maps for several observables, including, in
turn, the Higgs bosons, some superpartners and other collider
signatures, and finally dark matter cross sections.

 \begin{figure}[tbh!]
  \begin{center}
  \begin{tabular}{c c}
     \includegraphics[width=0.35\textwidth]{figures/m0_vs_m12_2D_mup_NMSSMlog.ps}
   & \includegraphics[width=0.35\textwidth]{figures/a0_vs_m0_2D_mup_NMSSMlog.ps}\\
     \includegraphics[width=0.35\textwidth]{figures/a0_vs_m12_2D_mup_NMSSMlog.ps}
   & \includegraphics[width=0.35\textwidth]{figures/tanb_vs_a0_2D_mup_NMSSMlog.ps}\\
     \includegraphics[width=0.35\textwidth]{figures/tanb_vs_m0_2D_mup_NMSSMlog.ps}
   & \includegraphics[width=0.35\textwidth]{figures/tanb_vs_m12_2D_mup_NMSSMlog.ps}\\
   \end{tabular}
  \includegraphics[width=0.3\textwidth]{figures/colorbar.ps}
  \end{center}
  \caption{\label{fig:CNMSSMps2dpdf_scan1} The 2D relative probability density
    functions in the planes spanned by the CNMSSM parameters $\mhalf$,
    $\mzero$, $\tanb$ and $\azero$ for the log prior.  The pdfs are normalized to unity
    at their peak. The inner (outer) blue solid contours delimit regions
    encompassing 68\% and 95\% of the total probability,
    respectively. All other basis parameters, both CNMSSM and SM ones,
   in each plane have been marginalized over (i.e., integrated
    out). Blue dots denote some best fit points. }
  \end{figure}

To begin with, in Fig.~\ref{fig:CNMSSMps2dpdf_scan1} we plot joint 2D
relative probability density functions (pdfs) for some combinations of
the CNMSSM parameters in our default case as given in
Table~\ref{table:prior} and taking the log prior, as explained above.
In this,  and figures below showing 2D pdfs, the inner (outer) contours
delineate the 68\% (95\%) total probability regions and the color code
is given in the bar at the bottom.

First, we can see that higher probability regions for all the
parameters but $\mzero$ are confined well within the assumed priors
and show clear high probability peaks. Focusing on the left panel in
the plane spanned by $\mhalf$ and $\mzero$, we can see some prominent
features: a rather strong preference for the stau coannihilation
region of $\mhalf\gsim\mzero\simeq0.5\mbox{ TeV}$, although the 68\% total
probability region extends to larger $\mzero$ because of the
pseudoscalar funnel effect contribution to $\abundchi$, and to much
larger values of the parameter of the focus point (FP)
region~\cite{Chan:1997bi,focuspoint-fmm}.
Green triangles indicate some of the best fit points.  The wedge
of $\mhalf\gg\mzero$ is disallowed because of charged LSP (normally
the stau).

Examining the other panels of Fig.~\ref{fig:CNMSSMps2dpdf_scan1} one
can see a rather strong preference for large $\tanb$ (as in the
CMSSM), although small values below some 15 are also
favored. $\azero$ appears to have two distinct branches of opposite
sign, with $\azero=0$, although not excluded, proving to be hard to
find solutions for, with some resemblance to the CMSSM.  In some sense
the latter may even be as favored as large positive values, as
indicated by one of the best fit points.

Clearly, these are familiar features of the CMSSM, as one can see by
comparing the high probability regions of the CNMSSM in
Fig.~\ref{fig:CNMSSMps2dpdf_scan1} with analogous figures for the
common set of parameters shared with the CMSSM, as shown in Fig.~13 of
Ref.~\cite{tfhrr1} (obtained with the NS scan), or with Fig.~1 of
Ref.~\cite{rrt3} (obtained with the MCMC scan).

The similarity of the high probability regions of $\mhalf$ and
$\mzero$ in both models suggests the parameters of the CNMSSM tend to
favor the decoupling limit, $\lambda \to 0$.  In
Fig.~\ref{fig:CNMSSM_lambda2dpdf_scan1} we show 2D pdfs of $\lambda$
with the CMSSM-like parameters. One can see that in
general $\lambda$ prefers to be small, which leads to a statistical
preference for a very CMSSM-like behavior.  Large values of $\lambda$,
bigger than around 0.6 are disfavored due to a Landau pole in the
running of $\lambda$. At ``intermediate'' values,
$0.1\lsim\lambda\lsim0.6$, the constraints become weaker but there
remain problems with tachyons, seen most clearly in the
$(\lambda,\kappa)$ plane, shown in Fig.~\ref{fig:lk}, which also shows
how both parameters are rather closely correlated, $\kappa \propto
\lambda $, and favor small values, towards the decoupling limit.  The
region with $\kappa\gg \lambda$ is disfavored by the presence of
tachyonic CP-odd scalars, and similarly with CP-even scalars for
$\kappa\ll \lambda$.
The
preference for low $\lambda$ could be due to the fact that there are
fewer tachyonic directions in the potential close to the decoupling
limit $\lambda \to 0$ (for this to happen $\lambda \lsim 0.1$ is
sufficient). For a more detailed discussion, see Ref.~\cite{Cerdeno:2004xw}.

In conclusion, the parameters of the CNMSSM seem to favor the CMSSM
limit since at small values of $\lambda \lsim 0.1$ it is simply much easier to find physical
solutions. This has been confirmed with exploratory runs with only the
requirement of correct EWSB and a neutralino LSP enforced.
Indeed, a flat (and nor a log) prior in $\lambda$ was
chosen so as not to  emphasize low values of the parameter
and instead to ``force'' the scan away from the decoupling limit. Even with
the flat prior, however, the preference for small $\lambda$ remains
strong. For $\lambda$ below $0.1$ there are more solutions because for
instance tachyons are less of a problem (due to less mixing with
singlets) and also we are further away from the Landau pole
region.

\begin{figure}[tbh!]
  \begin{center}
  \begin{tabular}{c c}
     \includegraphics[width=0.35\textwidth]{figures/lambda_vs_m12_2D_mup_NMSSMlog.ps}
    & \includegraphics[width=0.35\textwidth]{figures/lambda_vs_m0_2D_mup_NMSSMlog.ps}\\
     \includegraphics[width=0.35\textwidth]{figures/lambda_vs_tanb_2D_mup_NMSSMlog.ps}
     & \includegraphics[width=0.35\textwidth]{figures/lambda_vs_A0_2D_mup_NMSSMlog.ps}\\
   \end{tabular}
  \includegraphics[width=0.3\textwidth]{figures/colorbar.ps}
  \end{center}
\caption{\label{fig:CNMSSM_lambda2dpdf_scan1} The 2D relative
    probability density functions in the planes spanned by $\lambda$
    and the other CNMSSM parameters for the log prior.  The pdfs are
    normalized to unity at their peak. The inner (outer) blue solid
    contours delimit regions encompassing 68\% and 95\% of the total
    probability, respectively. All other basis parameters, both CNMSSM
    and SM ones, in each plane have been marginalized over. Blue dots
    denote some best fit points.}
  \end{figure}

\begin{figure}[tbh!]
\begin{center}
 \begin{tabular}{c}
    \includegraphics[width=0.35\textwidth]{figures/lambda_vs_kappa_2D_mup_NMSSMlog.ps}\\
  \includegraphics[width=0.3\textwidth]{figures/colorbar.ps}
  \end{tabular}
\end{center}
\caption{\label{fig:lk}
The 2D
relative pdfs in the plane of $(\lambda,\kappa)$ for the log prior.
}
\end{figure}

 \begin{figure}[tbh!]
  \begin{center}
  \begin{tabular}{c c}
     \includegraphics[width=0.35\textwidth]{figures/mu_vs_m12_2D_mup_NMSSMlog.ps}
    & \includegraphics[width=0.35\textwidth]{figures/mu_vs_m0_2D_mup_NMSSMlog.ps}\\
      \includegraphics[width=0.35\textwidth]{figures/mu_vs_tanb_2D_mup_NMSSMlog.ps}
     & \includegraphics[width=0.35\textwidth]{figures/mu_vs_A0_2D_mup_NMSSMlog.ps}\\
   \end{tabular}
  \includegraphics[width=0.3\textwidth]{figures/colorbar.ps}
  \end{center}
\caption{\label{fig:CNMSSM_mu2dpdf_scan1} The 2D relative probability
    density functions in the planes spanned by $\mu$ and the CNMSSM parameters
    that are the same for the CMSSM for the log
    prior.  The pdfs are normalized to unity at their peak. The inner
    (outer) blue solid contours delimit regions encompassing 68\% and
    95\% of the total probability, respectively. All other basis
    parameters, both CNMSSM and SM ones, in each plane have been
    marginalized over. Blue dots denote some
    best fit points.}
  \end{figure}

 \begin{figure}[tbh!]
  \begin{center}
  \begin{tabular}{c c}
     \includegraphics[width=0.35\textwidth]{figures/mchi_vs_ma1_2D_mup_NMSSMlog.ps}
    & \includegraphics[width=0.35\textwidth]{figures/mu_vs_ma1_2D_mup_NMSSMlog.ps}\\
   \end{tabular}
  \includegraphics[width=0.3\textwidth]{figures/colorbar.ps}
  \end{center}
\caption{\label{fig:CNMSSM_mumaone_scan1} The 2D relative probability
    density functions in the plane of $(\mchi,m_{a_1})$ (left panel)
    and $(\mu,m_{a_1})$ (right panel) for the log
    prior.  The pdfs are normalized to unity at their peak. The inner
    (outer) blue solid contours delimit regions encompassing 68\% and
    95\% of the total probability, respectively. All other basis
    parameters, both CNMSSM and SM ones, in each plane have been
    marginalized over. }
  \end{figure}

It is also instructive to show 2D probability maps of the effective $\mu$
parameter \vs\ some of the CNMSSM parameters. This is presented in
Fig.~\ref{fig:CNMSSM_mu2dpdf_scan1}. We can see that the consistency
of the model and the applied set of constraints favor $\mu$ below some
$2\mbox{ TeV}$, the range comparable to $\msusy$, as expected. In other
words, in the CNMSSM the $\mu$ problem is solved without any need for
additional fine tuning of parameters. We can also see an interesting
correlation with $\mhalf$ but not with the other
C(N)MSSM parameters. This is caused primarily by the CP-odd Higgs $a_1$
funnel effect and the fact that its mass is correlated with
$\mu$. These features are presented in Fig.~\ref{fig:CNMSSM_mumaone_scan1}.
Finally, in Fig.~\ref{fig:CNMSSMps1dpdf_scan1} we present 1D pdfs of several
key parameters which show more clearly their high probability ranges.

\begin{figure}[tbh!]
\begin{center}
\begin{tabular}{c c c c}
\includegraphics[width=0.245\textwidth]{figures/NMSSM-m12.ps}&
\includegraphics[width=0.245\textwidth]{figures/NMSSM-m0.ps}&
\includegraphics[width=0.245\textwidth]{figures/NMSSM-A0.ps}&
\includegraphics[width=0.245\textwidth]{figures/NMSSM-tanb.ps}\\
\includegraphics[width=0.245\textwidth]{figures/NMSSM-lambda.ps}&
\includegraphics[width=0.245\textwidth]{figures/NMSSM-mu.ps}&
\includegraphics[width=0.245\textwidth]{figures/NMSSM-kappa.ps}&
\includegraphics[width=0.245\textwidth]{figures/NMSSM-kappas.ps}\\
\end{tabular}
\end{center}
\caption{\label{fig:CNMSSMps1dpdf_scan1}
The 1D relative
probability densities for all the CNMSSM parameters, plus $\kappa$,
$\mu$, $\lambda s$ and $\kappa s$. }
\end{figure}

Prior dependence is often an issue in Bayesian statistics and needs to
be addressed. Even the CMSSM tends to be under-constrained which leads
to a fairly strong prior dependence~\cite{tfhrr1}, and in the NUHM,
with two extra parameters, the situation becomes
worse~\cite{nuhm1}. In the left panel of
Fig.~\ref{fig:CNMSSMps2dpdf_comp} we show a 2D pdf in the
($\mhalf,\mzero$) plane assuming the flat prior in all the CNMSSM
parameters. By comparing with the analogous panel of
Fig.~\ref{fig:CNMSSMps2dpdf_scan1} we indeed see a substantial shift
in the high probability region to larger values, as typical for the
flat prior due to the volume effect.

A related issues is that of the assumed range of input parameters. We
have already seen in the left panel of
Fig.~\ref{fig:CNMSSMps2dpdf_comp} that $\mzero$ was not well confined
to the assumed range below $4\mbox{ TeV}$. In order to examine this, in the
right panel of Fig.~\ref{fig:CNMSSMps2dpdf_comp} we show a 2D pdf in
the ($\mhalf,\mzero$) plane with greatly extended ranges of both
parameters ($50\mbox{ GeV}<\mhalf,\mzero<10\mbox{ TeV}$) and taking the log
prior. Clearly, there is basically no cap on the 95\% total
probability range in both parameters, although of course such large
values of soft mass parameters can hardly be considered as well
motivated in effective low-energy SUSY models.

\begin{figure}[tbh!]
 \begin{center}
  \begin{tabular}{c c}
  \includegraphics[width=0.35\textwidth]{figures/m0_vs_m12_2D_mup_NMSSMflat.ps}
   & \includegraphics[width=0.35\textwidth]{figures/m0_vs_m12_2D_mup_NMSSMlog10.ps}\\
   \end{tabular}
  \end{center}
 \caption{ \label{fig:CNMSSMps2dpdf_comp} The same as in
   fig.~\protect\ref{fig:CNMSSMps2dpdf_scan1} but for a flat prior
   (left panel) and a log prior with a greatly extended range,
   $50\mbox{ GeV}<\mhalf,\mzero<10\mbox{ TeV}$ (right panel).  }
 \end{figure}

\begin{figure}[tbh!]
\begin{center}
\begin{tabular}{c c}
 \includegraphics[width=0.35\textwidth]{figures/nmssm_m0_vs_m12_bino_log_3d.ps}
    & \includegraphics[width=0.35\textwidth]{figures/nmssm_m0_vs_m12_higgsino_log_3d.ps}\\
     \includegraphics[width=0.35\textwidth]{figures/nmssm_m0_vs_m12_mixed_log_3d.ps}
    & \includegraphics[width=0.35\textwidth]{figures/nmssm_m0_vs_m12_singlino_log_3d.ps}\\
\end{tabular}
\end{center}
\caption{\label{fig:CNMSSM3D_gaugino_scan1} In the plane of
  $(\mhalf,\mzero)$ for the log prior we show values of the gaugino
  fraction $Z_g=Z^2_{11}+Z^2_{12}$ (upper left panel), doublet higgsino
  fraction $Z_h=Z^2_{13}+Z^2_{14}$ (upper right panel), mixed region
  (lower left panel), as well as the singlino fraction
  $Z_s=Z^2_{15}$ (lower right panel).
Also shown are the 69\% (95\%)
  total probability regions from the upper left panel of
  Fig.~\protect{\ref{fig:CNMSSMps2dpdf_scan1}}. }
\end{figure}

We have already emphasized that the high probability regions of the
crucial parameters $\mhalf$ and $\mzero$ in the CNMSSM are quite
similar to the well studied CMSSM case. One of the key features of the
CMSSM is that the neutralino LSP is mostly a bino, except for the FP
region of large $\mzero$, where a larger admixture of the higgsino is
present. In the CNMSSM, with an additional singlet field whose mass is
controlled by $\kappa s$, the picture could in principle be very
different from the CMSSM.  We examine this in
Fig.~\ref{fig:CNMSSM3D_gaugino_scan1} where we separately show the
regions where the LSP is mostly gaugino ($Z_g=Z^2_{11}+Z^2_{12}>0.7$)
(left panel), doublet higgsino ($Z_h=Z^2_{13}+Z^2_{14}>0.7$) (middle
left panel), the mixed region ($0.3<Z_g,Z_h<0.7$ and
$Z_s=Z^2_{15}<0.5$) (middle right panel), as well as mostly singlino
($Z_s>0.5$) (right panel). (The wino component is always negligible
and below we will show only the bino fraction $Z_b=Z^2_{11}$.) We can
see that in an overwhelming fraction of cases the LSP still remains
predominantly bino-like. This is in agreement with the panel showing
$\kappa s$ in Fig.~\ref{fig:CNMSSMps1dpdf_scan1} where small values of
the product tend to be strongly disfavored.  We expose those non-CMSSM
like cases in Fig.~\ref{fig:CNMSSMps2dpdf_comp2}. Clearly, points
corresponding to singlino LSP cases exist but are rare.

\begin{figure}[tbh!]
 \begin{center}
  \includegraphics[width=0.35\textwidth]{figures/nmssm_m0_vs_m12_4tev_3d.ps}
 \includegraphics[width=0.35\textwidth]{figures/nmssm_m0_vs_m12_10tev_3d.ps}
  \end{center}
 \caption{ \label{fig:CNMSSMps2dpdf_comp2} A comparison of the bino ($Z_b>0.7$),
 doublet higgsino ($Z_h>0.7$), mixed ($0.3<Z_g,Z_h<0.7$ and $Z_s<0.5$) and singlino
 dominated ($Z_s>0.5$)  cases of the LSP in the plane spanned by $\mhalf$ and $\mzero$,
with our default case on the left hand side and with
 the log prior and much extended range of $10\mbox{ TeV}$ on the right. Also
 shown are the 69\% (95\%)   total probability regions.}
 \end{figure}

Similarly to the CMSSM, the key observables shaping the high
probability regions of the model are: $\abundchi$, $\brbsgamma$,
$\deltagmtwo$ and the light Higgs mass $\mhl$. Their 1D pdfs are
presented in Fig.~\ref{fig:NMSSM_oh2+bsg+gm2+mhl_1d}. We can see that,
apart from $\deltagmtwo$, they reproduce the likelihood rather well,
especially for our default log prior (long-dashed red curve), although
even for the flat prior the fit is not bad, except for $\deltagmtwo$, again with much
resemblance to the CMSSM~\cite{tfhrr1}.

The sharp cutoff in $\mhl$ at the LEP limit results from the
approximation that we have adopted, as mentioned above. Given the
complexities of the Higgs sector and a much larger list of possible
decay channels, we have taken an approximate approach of setting the
likelihood to one or zero for points that are accepted or excluded by
LEP data using the NMSPEC code. A more correct would would have
allowed for some ``tail'' at lower masses, as in the
CMSSM~\cite{rrt2}, and would have expanded allowed ranges of $\mhalf$
and $\mzero$ towards smaller values but this would have a limited
effect on this analysis in which we are mostly interested in
presenting mainly global features of the CNMSSM. Nevertheless, it is
worth stressing that in an exploratory run with the LEP limit smeared out
we have found only a few points for which
the singlet component is barely enough to escape the limit of
$114.4\mbox{ GeV}$. In this sense we expect that a full analysis would have
basically reproduced the case of the CMSSM~\cite{rrt2}.

\begin{figure}[tbh!]
\begin{center}
\begin{tabular}{c c}
\includegraphics[width=0.35\textwidth]{figures/nmssm_oh2} &
\includegraphics[width=0.35\textwidth]{figures/nmssm_bsg}\\
\includegraphics[width=0.35\textwidth]{figures/nmssm_gm2} &
\includegraphics[width=0.35\textwidth]{figures/nmssm_mh}
\end{tabular}
\end{center}
\caption{\label{fig:NMSSM_oh2+bsg+gm2+mhl_1d} The 1D relative
probability densities for $\abundchi$ (upper left panel), $\brbsgamma$
(upper right panel), $\deltagmtwo$ (lower left panel) and the light Higgs
mass $\mhl$ (lower right panel).  In each panel we show the posterior
for the flat prior (dotted blue) and the log prior (long-dashed red)
and the likelihood function (solid black). }
\end{figure}

The Higgs sector of the NMSSM contains three CP-even bosons $h_1\equiv
\hl$, $h_2$ and $h_3$, two CP-odd ones $a_1$ and $a_2$, as well as a
pair of the charged Higgs
$H^\pm$. Fig.~\ref{fig:CNMSSM_mhiggs_1d_scan1} shows the relative 1D
pdfs of $h_2$ (left panel), $a_1$ (middle panel) and $H^\pm$ (right
panel) for both our default log prior (long-dashed red) and the flat
prior (dotted blue) for comparison. We can see that the prior
dependence is not very strong, with the flat prior favoring larger
values, as usual. Also, by comparing with Fig.~5 of
Ref.~\cite{rrt2}, we can see that the pdfs are quite similar to the analogous
states in the CMSSM.

\begin{figure}[tbh!]
\begin{center}
\begin{tabular}{c c c}
  \includegraphics[width=0.33\textwidth]{figures/nmssm_mh2.ps}&
      \includegraphics[width=0.33\textwidth]{figures/nmssm_ma1.ps}
    & \includegraphics[width=0.33\textwidth]{figures/nmssm_mhpm.ps}
    \end{tabular}
\end{center}
\caption{\label{fig:CNMSSM_mhiggs_1d_scan1} The relative 1D pdfs of some of the
  Higgs masses: the second to lightest scalar $h_2$ (left panel), the
  lightest pseudoscalar $a_1$ (middle panel) and the charged Higgs
  $H^\pm$ (right panel). In each panel we show
the posterior for the flat prior (dotted blue) and the log prior
(long-dashed red).
}
\end{figure}

In Fig.~\ref{fig:NMSSM_mchi_1d} we present the relative 1D pdfs for
several superpartners, in a fashion similar to the previous
Figure. Again, we can see that the log prior gives somewhat lower
ranges of masses, especially for the scalars, which primarily depend
on $\mzero$ and that the distributions are rather similar to the
corresponding ones in the CMSSM; compare, eg, Fig.~17 of
Ref.~\cite{rtr1}.  It is clear that there will be a rather mixed
chance of detecting those states at the LHC. For example, with the
gluino to be probed up to some $2.7\mbox{ TeV}$, nearly
the whole range will be tested with the log prior, but much less so
with the flat prior. The scalars, on the other hand, will be much more
challenging for both priors.

In Table~\ref{table:best_fit} we list the best fit values for a number
of observables for our default log prior and also, for comparison, for
the flat prior. We stress, however, that the log prior appears more
appropriate for exploring unified low-energy SUSY models, as already
emphasized above.

  \begin{table}
   \centering
  \begin{tabular}{|l | c| c |}
  \hline
  Parameter & Best fit (log) & Best fit (flat) \\
  \hline
  \hline
  $\mhalf$ &  101\mbox{ GeV}&  478\mbox{ GeV}           \\
 $\mzero$ &  404\mbox{ GeV}&  632\mbox{ GeV}           \\
 $\azero$ &  -165\mbox{ GeV}& 1.20\mbox{ TeV}          \\
 $\tanb$ &  12.9 & 42.4  \\
   $\lambda$ &  0.009 & 0.0252 \\
 \hline
  $\mu$  & 547\mbox{ GeV}  & 672\mbox{ GeV}  \\
  $m_{a_1}$ & 274\mbox{ GeV}  & 476\mbox{ GeV}  \\
  \hline
  $\abundchi$ & 0.093 & 0.094    \\
  $\brbsgamma$ &  $3.10\times 10^{-4}$&  $3.27\times 10^{-4}$  \\
  $\brbsmumu$ &  $2.8\times 10^{-9}$&$1.6\times 10^{-8}$    \\
  $\brbtaunu$ &  $1.28\times 10^{-4}$& $0.93 \times 10^{-4}$   \\
  $\deltagmtwo$ & $16.9\times 10^{-10}$&  $14.8\times 10^{-10}$ \\
  $\mhl$ &  114.4\mbox{ GeV} & 114.3\mbox{ GeV}        \\
  $\mchi$ &164\mbox{ GeV} & 263\mbox{ GeV}  \\
 $m_{\chi^{\pm}_1}$ & 309\mbox{ GeV} & 491\mbox{ GeV}          \\
 $\mgluino$ & 950\mbox{ GeV} & 1.45\mbox{ TeV}  \\
  \hline
  $\chi2$&   9.6965&   9.4635    \\
  \hline
  \end{tabular}
  \caption{\label{table:best_fit} A table showing the values of various
   parameters for the best fitting point in both the log and flat prior
   case.}
  \end{table}

\begin{figure}[tbh!]
\begin{center}
\begin{tabular}{c c c}
     \includegraphics[width=0.33\textwidth]{figures/nmssm_mchi1.ps}
   & \includegraphics[width=0.33\textwidth]{figures/nmssm_mch1.ps}
   & \includegraphics[width=0.33\textwidth]{figures/nmssm_mg.ps}\\
      \includegraphics[width=0.33\textwidth]{figures/nmssm_mst1.ps}
   & \includegraphics[width=0.33\textwidth]{figures/nmssm_mss1.ps}
   & \includegraphics[width=0.33\textwidth]{figures/nmssm_mstau1.ps}\\
\end{tabular}
\end{center}
\caption{\label{fig:NMSSM_mchi_1d} The 1D relative probability
densities for the mass of the lightest neutralino $\mchi$ (upper left
panel), the lightest chargino $\mcharone$ (upper middle panel), the
gluino $\mgluino$ (upper right panel), the lighter stop $\stopone$
(lower left panel), left squark $\tilde{q}_L$ (lower middle panel) and
the lighter stau $\stauone$ (lower right panel). In each panel we show
the posterior for the flat prior (dotted blue) and the log prior
(long-dashed red).  }
\end{figure}

Finally, we move to discussing the model's predictions for the
detection of the lightest neutralino assumed to be the DM in the
Universe in direct detection searches via its elastic scatterings with
targets in underground detectors. We follow the same procedure and
formalism as previously in~\cite{rtr1,rrt3,tfhrr1}.  The underlying
formalism can be found in several sources, {\it e.g.}, in
Refs.~\cite{dn93scatt:ref,susy-dm-reviews,efo00,knrr1}.

In Fig.~\ref{fig:sigsip_1d} we present the 2D posterior pdfs in the
usual plane spanned by the spin-independent cross section $\sigsip$
and the neutralino mass $\mchi$. The left (right) panel corresponds to
the log (flat) prior.  For comparison, some of the most stringent
90\%~CL experimental upper limits are also marked~\cite{cdms-sep05,
edelweiss-one-final, zeplin-one-final, zeplin2, zeplin3, xenon-10},
although they have not been imposed in the likelihood, as before in
our studies of the CMSSM, because of substantial astrophysical
uncertainties, especially in the figure for the local density.

Several key features can be seen in Fig.~\ref{fig:sigsip_1d}. Firstly,
the prior dependence is not very strong for both 68\% and 95\% total
probability regions, which is encouraging. It does
not affect much the banana-shape high-probability region which
corresponds to the Higgs funnel and the stau coannihilation
regions. The horizontal branch of $\sigsip\simeq 7\times 10^{-8}\pb$
is more affected because it corresponds to the focus point region of
large $\mzero$. Next, the overall shape rather closely resembles the
case of the CMSSM, see, {\it e.g.}, Fig.~18 of Ref.~\cite{tfhrr1} or  Fig.~13
of Ref.~\cite{rtr1}. (The slight upwards shift in $\sigsip$ results
from changing the code from DarkSusy to Micromegas.) It does, on the
other hand, differ from the predictions of the NUHM which features an
additional higgsino-like region at $\mchi\sim 1\mbox{ TeV}$; see Fig.~12 of Ref.~\cite{nuhm1}.

Independently of the prior, basically the whole 68\% and 95\% total
probability regions are likely to be within the planned reach of
$10^{-10}\pm$ of future 1-tonne detectors. Some of the currently
operating detectors are already probing some of the high probability
regions, and with a ``modest'' improvement down to $\sim 10^{-8}\pb$,
they will be testing some of the most likely cross sections.

\begin{figure}[tbh!]
\begin{center}
\begin{tabular}{c c}
   \includegraphics[width=0.35\textwidth]{figures/DDsip_vs_mchi_mup_NMSSM.ps}
  & \includegraphics[width=0.35\textwidth]{figures/DDsip_vs_mchi_mup_NMSSMflat.ps}
\end{tabular}
  \includegraphics[width=0.3\textwidth]{figures/colorbar.ps}
\end{center}
\caption{\label{fig:sigsip_1d} For the dark matter spin-independent
  cross section $\sigsip$ \vs\ the neutralino mass $\mchi$ we show the
  2D relative probability density for the log prior
  (left panel) and the flat prior (right panel).
}
\end{figure}

\section{Conclusions and summary}\label{sec:summary}

The Next-to-Minimal Supersymmetric Standard Model solves the
$\mu$-problem of the MSSM but, without grand unification,  both
models suffer from a large number of parameters. The constrained
versions of both models are in this respect much more
well-motivated. Because of the additional singlet superfield present
in the CNMSSM, the resulting phenomenology in the Higgs and neutralino
sectors is considerably richer. Therefore, a prior one could expect
that the models could be distinguished in experimental tests.

The global exploration of wide ranges of CNMSSM parameters and a
Bayesian analysis show that, from the statistical point of view, this
is not the case. The coupling $\lambda$ strongly favors as small
values as possible, in other words it tends towards the decoupling
regime in which one recovers the CMSSM plus the basically decoupled
singlet Higgs and the singlino. As a result, Higgs and superpartner
mass spectra also tend to resemble those of the CMSSM, as does the
cross section for direct detection of neutralino dark matter.
Nevertheless, we have identified a limited number of cases where the
LSP is indeed singlino-dominated, but statistically they are not very
significant.

In conclusion, the CNMSSM is, for the most part, testable at the LHC
and in dark matter searches, which is certainly encouraging. On the
other hand, should a CMSSM-like signal be detected, it is likely to be very
challenging to distinguish between the two models.

\medskip
{\bf Acknowledgments} \\ LR is partially supported by the EC 6th
Framework Programmes MRTN-CT-2004-503369 and MRTN-CT-2006-035505.
RRdA is supported by the project PARSIFAL (FPA2007-60323) of the
Ministerio de Educaci\'{o}n y Ciencia of Spain. DL-F and TV are supported by
STFC.  The use of the Iceberg computer cluster at the
University of Sheffield is gratefully acknowledged. LR would like to
thank the CERN Theory Division for hospitality during the final stages
of the project.

redpajama_set_name: RedPajamaArXiv


text:
Goole was a parliamentary constituency centred on the town of Goole in the West Riding of Yorkshire which returned one Member of Parliament (MP) to the House of Commons of the Parliament of the United Kingdom, elected by the first-past-the-post voting system.

It was created for the 1950 general election, and abolished for the 1983 general election.

Boundaries
The Municipal Borough of Goole, the Urban District of Knottingley, and the Rural Districts of Goole, Osgoldcross, and Thorne.

Members of Parliament

Election results

Elections in the 1950s

Elections in the 1960s

Elections in the 1970s

References

External links

Parliamentary constituencies in Yorkshire and the Humber (historic)
Constituencies of the Parliament of the United Kingdom established in 1950
Constituencies of the Parliament of the United Kingdom disestablished in 1983
Goole

redpajama_set_name: RedPajamaWikipedia


text:
Category Archives: Indo-Pacific
"Wash Brains, Cleanse Hearts": Evidence from Chinese Government Documents about the Nature and Extent of Xinjiang's Extrajudicial Internment Campaign
Posted on November 24, 2019 by Adrian Zenz
Women undergoing "reeducation" in Xinjiang Uyghur Autonomous Region (XUAR, China) were kept in their classroom behind a gated metal fence. See Figure 16, below. Source: anonymous informant.
In the wake of growing international criticism, the Chinese government has sought to counter human rights accusations over its re-education and internment campaign in Xinjiang through an elaborate propaganda campaign. This campaign portrays the region's network of so-called "Vocational Skills Education Training Centers" (zhiye jineng jiaoyu peixun zhongxin 职业技能教育培训中心) as benign training institutions that offer persons who committed minor offenses an alternative to formal prosecution. Since late 2018, the state has invited media and official representatives from other nations and even from the western media to participate in official and closely-chaperoned tours of a select number of "showcase" centers.[1]
Drawing on the government's own statements, this article seeks decisively to refute these propaganda claims. Overall, the author analyzed three types of data sources, all of which are mutually consistent and confirm the growing body of first-hand witness accounts. The first type consisted of official government documents and related media reports that are publicly accessible but not designed for international audiences. The second source consists of local government data in the form of detailed tables and spreadsheets that list the fates of thousands of minority individuals. The third source is a confidential, classified Chinese policy document issued by the Xinjiang Uyghur Autonomous Region's Party Political and Legal Affairs Committee. This highly significant document details how Xinjiang's so-called "vocational training centers" are supposed to be run.
In combination, these three sources provide us with unprecedented insights into the region's re-education internment campaign. Together, they decisively refute Beijing's propaganda claims.
In this article, Xinjiang's "Vocational Skills Education Training Centers" are referred to as "Vocational Training Internment Camps" (VTICs). This terminology acknowledges that these facilities offer some form of vocational training, although this "training" only constitutes a relatively small part of the whole indoctrination package. At the same time, this terminology clarifies that these extrajudicial facilities function in a prison-like internment fashion.
Specifically, this article will show the following:
According to government statements, VTICs "wash clean the brains" of those interned in them. Those subjected to such coerced brainwashing are referred to as "re-education persons" – the same term used for detained Falun Gong practitioners. The classified document states that detainees who show signs of resistance are to be subjected to "assault-style re-education" efforts.
Specifically, those interned in VTICs are called "detained re-education persons". Numerous documents make clear that these "trainees" are in involuntary detention. Despite extensive research, the author did not even find a single government document that supports government claims that people willingly consent to being placed into a VTIC, that they sign any kind of agreement to that end, or that they can request leave. The classified document mandates special security measures to ensure that detainees cannot "escape" while relatives visit them in the camps.
VTICs are guarded by large, dedicated police units, including armed police forces. In one case, the number of security guards was over twice as high as that of the camp's teaching staff. In another county, the wages of the designated VTIC police force were budgeted to be nearly three times as high as this county's entire regular vocational education budget. Government regulations and the classified document both specify that VTICs must implement "escape prevention" measures that also apply to prisons. The classified source adds that VTICs must have dedicated police stations, should employ only the "most capable security forces", and put extremely stringent security and surveillance measures in place.
VTICs are administered by newly established "education and training bureaus" (ETBs) that fall under the authority of the criminal justice system and are funded from domestic security budgets. They are neither funded nor managed by the regular education system. The classified document mandates that every county in Xinjiang must have an ETB. Based on the new data, the author estimates that Xinjiang likely has approximately 1,300 to 1,400 extrajudicial internment facilities.
VTICs represent only one of up to 8 forms of extrajudicial internment in Xinjiang. Detailed local government data sets show that the internment campaign has mostly swept up males, especially household heads. Internment shares in rural Uyghur majority regions (including those sentenced to prison) range between 10 and 30 percent of the adult population. In 2018, the Xinjiang government provided 1.6 billion RMB in VTIC food subsidies to its ethnic minority regions, enough to feed just under one million persons in this particular form of extrajudicial internment alone.
Evidence shows that the internment drive has focused on removing male authority figures from families as part of the state's coercive social re-engineering campaign. Internment shares of younger women, who often feature in propaganda videos or "model camps," are typically very low. Consequently, interned populations feature a much higher share of adults aged 40 or higher than those who are not interned.
Overall, the author suggests a new speculative upper limit estimate of 1.8 million or 15.4 percent of adult members of Xinjiang's Turkic and Hui ethnic minority groups, and a new minimum estimate of 900,000 or 7.7 percent. These figures pertain to all minority adults in previous (since spring 2017) or current extrajudicial internment. While still speculative, the new upper limit is eminently defensible based on existing and new data sets.
Official data proves that the internment campaign has pushed families below the poverty line by depriving them of their primary labor force, and that net population growth rates in southern Xinjiang have dramatically declined since the beginning of the internments.
The classified document specifies that "students" can only "complete their studies" after having spent at least one year in the facilities. Only once they have fulfilled a detailed set of stringent "graduation" criteria do they actually receive an intensive 3-6 months of skills training. This would indicate a minimum term at the VTICs of 15-18 months, which is consistent with the time between the onset of the re-education campaign (April 2017) and the first propaganda videos published on Chinese media channels showing the "successful outcomes" of the camps (October 2018).
According to the classified document, the Xinjiang government considers VTIC work to be "highly sensitive" in nature. All related information is "strictly confidential" and VTIC data material "must not be aggregated" even by its own staff, likely in order to conceal the scale of the internment campaign.
Chinese claims that Xinjiang has no "re-education camps" are simultaneously true and false. They are superficially true in that such denials use a Chinese term for "re-education" that the government itself never employs. However, they are also manifestly false, given there is abundant evidence from government documents that there are several types of dedicated re-education facilities in Xinjiang, and that the officially-stated primary goal of the VTICs is not "vocational training" but "transformation through education". Government claims that Xinjiang has no "concentration camps" are both semantically and technically false, and contradicted by the state's own terminology. Even so, the author suggests that the term "re-education camps" (or "internment camps") is more accurate and helpful.
As China's internment and related propaganda campaign progresses, this article provides crucial incriminating evidence about the real nature and purpose of the region's VTIC network. The empirical evidence discussed below should suffice to support significant, concrete actions by the international community against this unprecedented atrocity.
Posted in Article, Asia, Asia-Pacific, Assimilation, Authoritarianism, Censorship, China, China, Communism, East Turkestan, Ethics, Ethnicity, Human Rights, Indo-Pacific, Migration, Military Strategy, National Security, Nationalism, Political Ethics, Prisons, Qualitative, Quantitative, Security, Separatism, Social Movements, Strategy, Uncategorized, Xinjiang
Democratizing China Should Be The U.S. Priority
Protestors hold placards and illuminated smartphones beside a large banner calling for democracy during a protest in Hong Kong, China, on June 26, 2019. Some protesters held signs calling on U.S. President Donald Trump to save Hong Kong. Paul Yeung/Bloomberg via Getty Images
U.S. goals in relation to China, our biggest national security threat, tend to array along three main axes: military, diplomatic, and economic. But in deference to the failed strategy of engagement, we don't use the significant normative and ideological power of democratization as a multiplier on these battlefields, nor does the prospect of democratizing China factor sufficiently in our cost-benefit analyses.
Militarily, we prioritize defense from China, but other than ongoing military support to Taiwan and the Tibet campaign of 1957-72,[1] we have not used our substantial military resources to promote democracy in China, for example in the rebellious zones of Xinjiang or Hong Kong. Economically, we prioritize U.S. market share in China, IP protection, and beating China's GDP, technology and industrial strength. But we don't condition our China trade on our lowest priorities, human rights and democracy.
In the short term our military and economic priorities are correct, but given the Chinese Communist Party's growing strength globally, we must increase the prioritization of democracy as a long-term end goal in China, and we need to reevaluate opportunities to use our still substantial but relatively diminishing military and economic power to bring democracy to China. Continue reading →
Posted in Aerospace Defense, Alliances, Americas, Arms, Asia, Asia-Pacific, Authoritarianism, Canada, Censorship, China, China, Communism, Communism, Democracy, Democratic Peace Theory, Deterrence, Diplomacy, East Asia, East Turkestan, Economic Sanctions, Economic Security, Economics, Electoral, Electoral Politics, Engagement, Europe, European Union, European Union, France, GDP, Global, Hong Kong, Hypersonic, Indo-Pacific, Influence Operations, Insurgency, Intelligence, International Conflict, International Law, Iran, Iran, Japan, Japan, Lobbying, Military, Military Strategy, National Security, NATO, Naval Warfare, Negotiation, Norms, North America, North Korea, North Korea, Nuclear Weapons, Opinion, Politics, Qualitative, Rule of Law, Russia, Russia, Sanctions, Security, Separatism, South Korea, sovereignty, Special Interests, Strategy, Syria, Taiwan, Tariffs, Theory, Tibet, Trade, Trade, Trade, Trade War, United States, United States of America, USA, USINDOPACOM, Weapons, WMD, Xinjiang
Geopolitics and the Western Pacific: An Interview with Leszek Buszynski
The book cover of Geopolitics and the Western Pacific: China, Japan and the US, by Dr. Leszek Buszynski. Routledge, 2019.
This interview with Dr. Leszek Buszynski, author of Geopolitics and the Western Pacific: China, Japan and the U.S. (Routledge, 2019), took place by email with Dr. Anders Corr between May 31 and June 12.
Anders: What are some of your recommendations in the book?
Leszek: The recommendations are in the final chapter and have been written from the perspective of Australia as a a middle power and ally of the US. Basically, the U.S. relies excessively on military power to counter China but this is creating the fear of a US-China clash in the region from which China benefits, particularly within ASEAN. Scuttling the Trans-Pacific Partnership (TPP) was a mistake because it is a way of bringing together the states of the region into cooperation with the U.S., Japan and Australia in a way which would offset Chinese influence.
Anders: Don't you think that China is also creating fear with its military buildup? Wouldn't countries like Japan and South Korea be even more fearful if they did not have the U.S. military there to protect them?
Leszek: This is not the issue, the answer is of course. But without a broader US presence in the region, one that is not just military based, regional countries such as those in ASEAN would feel the pressure to gravitate to China. China has a way of undermining the U.S. presence and its alliance system by playing on regional fears of conflict and instability, the Philippines under Rodrigo Duterte is a case in point. America has to counteract that. Continue reading →
Posted in Aerospace Defense, Alliances, Americas, ASEAN, Asia, Asia-Pacific, Australia, Authoritarianism, Book Review, China, China, Communism, Communism, Corruption, Debt, Democracy, Democratic Party, Democratic Party, Deterrence, Diplomacy, East Asia, Economic Sanctions, Economic Security, Economics, Energy, Export Restrictions, FDI, Freedom of Navigation, Global, History, Human Rights, India, India, Indo-Pacific, Indonesia, Indonesia, Influence Operations, Infrastructure, Infrastructure, International Conflict, International Law, International Organizations, Interview, Investment, Japan, Japan, Law of the Sea, Liberalism, Loans, Manufacturing, Military, Military Strategy, National Security, Nonalignment, North America, Oil & Gas, Politics, Protectionism, Qualitative, RCEP, Republican Party, Republican Party, Russia, Russia, Sanctions, SCO, Security, Shipping, Socialism, South Asia, South China Sea, South Korea, South Pacific, Special Interests, Steel, Strategy, Supply Chains, Tariffs, Taxation, Technology, TPP, TPP-11, Trade, Trade, Trade, Trade Agreements, Trade War, United States, United States of America, USA, USINDOPACOM, Vietnam

redpajama_set_name: RedPajamaCommonCrawl


A hard Brexit with no deal might well hit sandwich prices. This is because of unavoidable issues in the supply chain of certain foodstuff categories that would lead to price rises for certain types of food. Among these are salad ingredients, chicken and other popular sandwich fillings that would leave the sandwich industry exposed to shortages or significant price increases.
It is becoming increasingly more likely that negotiations, or the lack of them, will result in a hard Brexit with no deal acceptable to both the EU and the UK. In such a case it is almost certain that the UK will lose out with increased prices in certain sectors. It is becoming increasingly obvious that certain bodies are now planning for a 'no Brexit deal' outcome. UK government ministers are continuing to maintain their optimism that a mutually acceptable deal will be struck. However, that is not the way that EU negotiators are looking at it.
What goes between two slices of bread is more important than the bread itself. The image of foodstuff stockpiling by the UK government is no longer implausible. In fact, it is becoming increasingly more likely that the illusion of warehouses full of lettuce, tomatoes, chicken and mayonnaise will be more than just a mirage of the mind. The chimera is no longer a fantasy, but a potential reality.
So what would be the result of this other than increased sandwich prices? A hard Brexit would benefit nobody, yet both sides recently appear set on making that the likely outcome of negotiations – although there appears to be little negotiating and more demands being made by each side of the English Channel.
That said, the likelihood of food stockpiling is a very low one. There is insufficient slack in the food supply chain to enable this to be feasible. A hard Brexit may hit sandwich prices, but it would not be a consequence that could easily be avoided. Certainly not by stockpiling what are generally perishable goods! It is possible for the UK to extend Article 50. This would take pressure off price increases, though increase the pressure on politicians.
A hard Brexit or even no Brexit deal at all could hit food prices hard. However, it's unlikely for issues with the food supply chain to significantly increase sandwich prices. Greggs would not allow it!
I read this article and found it very interesting, thought it might be something for you. The article is called Hard Brexit May Hit Sandwich Prices Due to Food Supply Chain Issues and is located at https://marketresearch.biz/news/hard-brexit/.


Sometimes you can find the best images in your own front yard. A mighty maple tree in the front yard of our house and studio in the autumn season. A point of view showing the bark, trunk and leaves on the ground. I like the mightiness of trunk going into the ground. Hope you like it too.


text:
CDPS may refer to:

Cirencester Deer Park School
Cooperative distributed problem solving


Use these sprite font sheets to make your game look great and colorful!
Included is several font types and many color variations (96 sheets in total) and some Game Maker sprites, an object and instructions (see room creation code comments) to get you started quickly.
The image above is from the GM project.
Save time. Be cool, Buy this asset.
Don't forget to check my other assets out!.
Well worth the 99 Cents. Saved me loads of time drawing my own font. This is exactly what i wanted and it's great quality. Thank you!!


Asia is a rising market for agricultural products. Its rapid economic development and being the most populated of all continents, has led to an increasing demand for quality agricultural products.
AgriPro Asia's host city, Hong Kong, is one of the busiest trade hubs for agricultural products. Even more importantly, it is a free port and renowned as an "open market" with few trade barriers.
AgriPro Asia is a gateway to important markets such as China and South East Asia.


Brows and lashes are serious business. If I had to choose between the two, brows would trump my lash game any day. Prescription products designed to enhance brow and lash growth make me nervous with their side effects. I'm convinced if it's going to happen, it will happen to me. Cue Hydropeptide Lash claiming longer, fuller, lusher lashes… and brows.
Lash is a drug-free natural enhancer with a peptide complex to improve the appearance of brows and lashes by strengthening them for a fuller, longer, less brittle appearance. Basically, the serum is creating a healthy environment for your hair, like using treatments on your mane after coloring. By doing so you're going to experience less fallout and shedding, aiding in a fuller look.
I didn't notice my lash line appearing fuller, but they were fortified. Normally I could tug on my lashes and a few would come out, but not while consistently using the serum. But on my brows, it was much more obvious. Within 4 weeks I noticed a difference in how full my brows appeared, and with continued use it only improved. After dying and trimming I started receiving comments on how my brows looked, asking what I was doing differently. Within a few weeks of running out my brows are beginning to look sparse again, particularly the tails.
For best results this should be used daily, in the evening, or else you may be disappointed. Before toning or doing anything else to your skin apply the serum directly to your brows and lash line. Once you start layering your products avoid the brow area where serum was applied.
Eyelash Fortifying Peptides and Hair-Fullness Peptide work on a cellular level to nourish hair.
Biotin, Folic Acid, Hydrogenated Lecithin, and Lemon Peel Extract to help prevent breakage and strengthen hair.
On the left is my baseline. On the right 4 weeks after Hydropeptide Lash treatment, you can see sparse areas have filled in, brows are more full. Especially the tail!
On the left is the same photo above after 4 weeks of Hydropeptide Lash treatment. On the right brows have been trimmed and dyed.


This webcam is currently assigned to MatTru. It was originally added on 西元2008年12月01日 and has been viewed 141,238 times since then. The current picture above was taken 13 分鐘前, thereby the webcam seems to be currently active. So far, it was added to their personal favorites on webcams.travel by 2 people.


text:
Liberty Attendance Center - Class of 1969
Class Reunion - Class of 1969 - Liberty, Mississippi
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CBHC / RCAHMW > News > World Religion Day: 16th January 2022
World Religion Day: 16th January 2022
World Religion Day is celebrated on the third Sunday in January every year and is a reminder of the need for harmony and understanding between religions and faith systems. On this day, communities of different faiths have the opportunity to get together and listen to each other, as well as celebrate their differences and similarities.
World Religion Day is about understanding and religious tolerance. In Wales, the Toleration Act of 1689 allowed Protestants outside the Anglican Church freedom of worship. This freedom was soon translated into buildings, the ancestors of the nonconformist chapel which many regard as the national architecture of Wales. The earliest surviving chapel built as a result of the Toleration Act is Maeryronnen Congregational Chapel, this year celebrating its 325th anniversary. This Radnorshire chapel can be precisely dated to 1697, when it was registered at the assizes as a place of worship under the terms of the Toleration Act.
Maesyronnen is a substantial but low-key vernacular building that does not advertise its presence. Its seclusion is partly explained by the closed fellowship of the nonconformist Independents but also by the prejudice against members of the denomination who were widely regarded as 'king killers' after the execution of Charles I. The conversion of Maesyronnen farmhouse was an example of the prevailing attitude of 'make do and mend' which led to the adaption of buildings rather than demolition and new building. The original farmhouse was replanned as a chapel-house with a central doorway, while the attached cowhouse was thoroughly rebuilt as a chapel. A medieval cruck-truss is still embedded in the rear of the chimney stack between house and chapel. Although the meeting house is not overly ostentatious, internally it was, and is, full of furniture and artefacts of good craftmanship. These include the mullion and high-transomed windows, the pulpit, the box pews, and the communion table.
Built in 1697, Maesyronnen is an early example of 'toleration' but many other types of religious building co-exist in Wales today and enrich our contemporary culture. Readers may also be interested in recent blogs written by our Secretary/CEO Christopher Catling on the Shri Swaminarayan Mandir, Cardiff, one of the UK's most beautiful Hindu temples and Wales's first purpose-built mosque, the Noor-ul-Islam Mosque in Maria Street, Butetown, as well as a blog on the Grade II listed Merthyr Tydfil Synagogue, Recording the Last Synagogue of the Welsh Valleys by Susan Fielding.
This gallery of images shows the splendid variety of religious buildings in contemporary Wales.
Maesyronnen Congregational Chapel, built in 1697.
The interior of Maesyronnen Chapel with many of its fittings of good craftmanship.
The Noor-ul-Islam Mosque in Maria Street, Butetown,. Wales's first purpose-built mosque built in 1947.
Shri Swaminarayan Hindu Temple, Cardiff, opened in 1982. It acquired its distinctive appearance following major refurbishment work between 2005 and 2007.
The Church of Jesus Christ of Latter Day Saints, Cwmbran, as featured in the Royal Commission's recent study on Cwmbran and available as a free eBook.
Gurdwara Nanak Darbar Sikh Temple, Copper Street, Adamsdown, Cardiff. Built in 1871 as the Star Street English Independent Chapel (United Reformed Church), in 1996 the chapel was converted for use as a Sikh temple.
Merthyr Synagogue built in 1876 to serve a religious community of about 400 who lived and worked in Merthyr during the 1880s and '90s.
The oldest surviving synagogue in Wales recorded for posterity to millimetre accuracy as a result of recording work commissioned by the Royal Commission in partnership with the Foundation for Jewish Heritage.
With much of the early fabric dating from 1180 to 1220, St David's Cathedral is regarded as the most important medieval ecclesiastical building in Wales.
A Renaissance pendant in the nave ceiling at St David's dated by the Royal Commission to the 1530s just before the Reformation.
By Nicola Roberts, Communications Manager
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Spectacular architecture, thank you Nicola.


Amy Worth, 2019 president of the Realtor Association of Sarasota and Manatee, said that buyers don't like economic uncertainty.
"The government shutdown can be a cause for hesitation among buyers, especially if there are no clear signs of when the shutdown might end," Worth said.
Joanne Owens, broker/owner with Keller Williams on the Water in Bradenton, said she knows of two potential buyers who are directly affected by the shutdown.
But concerns extend much wider.
"Buyers who are not directly affected are very concerned about the fallout when the government gets back to work. Some have put their purchasing on hold for another year," Owens said.
The two buyers Owens knows who are directly affected by the shutdown are federal employees who are on furlough.
"They are concerned by the state of the financial situation and have put their purchase on hold," Owens said.
January is traditionally one of the busiest real estate sales months of the year in the Bradenton-Sarasota area, where many of the sales are cash deals.
Janet K. Robinson, commercial director for Florida West Coast Coldwell Banker Commercial NRT, said the shutdown is affecting Small Business Association loans.
SBA loans only require businesses to put 10 percent down, helping them to maintain more liquidity, she said.
"It does affect small businesses even if they are financing an improvement. It has put a lot of strategic planning on hold," Robinson said.
Also affected by the partial government shutdown is fund investment in designated opportunity zones, including several in Manatee County.
Because of the shutdown, the federal government canceled a public hearing on tax breaks available to funds that invest in economically depressed areas.
Images of the problems with human waste and trash due to a partial federal government shutdown are seen on social media.


At St Clare's learning is relevant and connected through Faith Life Inquiry, where scripture and the teachings of Jesus align with knowledge acquisition and the application of skills to create new learning and understandings, and explicit links across the curriculum.
We follow a personalised approach to learning with clearly defined Learning and Teaching Design Principles that guide all our endeavours.
In personalising the learning for our community of students we focus on building success for all. Pre-assessments and ongoing formative assessment target starting points for learning and monitor the progress of each student. Learning intentions are explicitly stated in student friendly language and success criteria give clarity to the achievement of the intentions. The implementation of varied teaching strategies and activities promotes engagement and challenge and encourages independence and self regulation as students make informed choices about their learning. Student voice and the opportunity to set goals and reflect on learning fosters ownership and builds partnerships across the school and wider community.
Thinking is not only a matter of skills but also a matter of dispositions. We foster open-mindedness, collaboration, curiosity, flexibility, persistence, independence, imagination and resilience.
The development of thinking is a social process. We provide balance between individual and group interactions and encourage the sharing of ideas and expertise.
Thinking is visible. Students and leaders of learning articulate, document and track their thinking.
The culture within our learning areas sets the tone for learning and shapes what is learned.
Our school has a culture of thinking and reflection.
At St Clare's open learning spaces are reflective of our educational philosophy where students learn through collaboration, self management and challenge. The learning spaces enable flexibility, student choice, rich dialogue, integration of curriculum and more individualised and small group instruction. Moreover the spaces are reflective of our contemporary society and support relevant and targeted learning. Learning is a social process and our approach provides opportunities for student access to a broad range of perspectives and expertise as well as building personal and interpersonal skills central to living in our modern society.


On Wednesday, the whole school went to the Cathedral to celebrate the Mass of the Risen Lord. A huge thank you to all parents and members of our parish comity who donated flowers which then decorated our cross.
The cross was taken down to the cathedral for the Mass, paraded back to school and stood out the front so that all who passed could witness that we are 'Easter People'. Children took part in the mass by doing readings, singing hymns and leading the prayers of Intersessions. Thank you to all who helped to bring the mass together.
Dancers from Year 5 and 6 took part in the Dance House Performance at The Alexandra Theater on Tuesday 25th April.
It is a local Arts driven initiative dedicated to supporting and encouraging the development of innovative and exciting dance. One of their aims is to provide performance opportunities for young people outside of the classroom and to experience the workings of a professional theatre.
The Dance House evenings celebrate the hard work, commitment and skill of young people within our vibrant community. It is an opportunity to share their dance work with an audience, as well as other schools, in a positive collaboration with professional artists and theatre technicians.
The girls performed really well and represented the school to the highest standard. Thank you to Charlie Ranken – our dance club teacher – for choreographing the piece and lending so much support to the girls.
Year 4 told the school the story of the trail and it was all done through poem and song that Mr Caws had written. It was very moving and the children loved every minute of it.
Year 6 then told the story of the crucifixion. We then sang the final part of 'Were you there' and after Jesus was buried in the tomb, the whole school left the hall in silence for the Easter Break.
On Thursday 6th April, Year 3 showed the rest of the school their Holy week Liturgy of The Last Supper.
On Wednesday, as part of our Holy week liturgies, Year 2 showed the rest of the school the part of the Easter story where Jesus washes the feet.
Jesus and His disciples were getting ready for the Passover Festival. Jesus knew that it was almost time for Him to leave His home on Earth and go back to Heaven. While they were eating dinner Jesus had a lot of things on His mind. He knew that one of His friends was going to betray Him. He also knew that God had a plan and had everything under control.
On Tuesday's Holy Week liturgy, Year 5 retold the story of the anointing at Bethany and Year 1 Acted out the Betrayal of Jesus. The whole school then sang 'Thirty pieces of silver' written by Mr caws.
Last Friday, the whole school was fully immersed in a day reflecting and nurturing their spirituality and sense of wonder. Workshops included children writing prayers, learning about refugees, making religious bookmarks and hearing about mission work in South Africa.
The children experienced four workshops and had the chance to work with different teachers and adults including volunteers from Yapton Free Church. This was an inclusive day where all children and adults were given the opportunity to further develop their spiritual relationship with Christ.
Many thanks to all involved and those who gave their free time to help organise and run the day!


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Hatty & Jaziel | Felisitasyon!!
I've known Jaziel for may years, and there is no way I would have ever thought that 24 years later, I would be shooting his engagement session. Boy, do I feel old!! I know I am not the only one that feels very, VERY happy for both him and Hatty. I know it sounds cliché, but seriously, if you know these two, you just know they are perfect for each other. It truly is a wonderful blessing from Jehovah to be able to find that one special person that shares the same love for Him and the same spiritual goals.
From Francis and I, we love you guys!!!
I just LOVE this happy shot!
Sweet kiss photos are may favorites, and with a background like this?! who can resist?!